Hoping to close the book on bounties, the NFL suspended New Orleans Saints defensive captain Jonathan Vilma without pay for all of next season Wednesday and gave shorter bans to three other players for their leading roles in the team’s cash-for-hits system that knocked key opponents out of games from 2009-11.

Defensive lineman Anthony Hargrove, now with the Green Bay Packers, was suspended for the first half of the 16-game season; Saints defensive end Will Smith was barred for the opening four games; and linebacker Scott Fujita, now with the Cleveland Browns, will miss the first three games of 2012. Like Vilma, they were suspended without pay, costing each hundreds of thousands of dollars.

The league said its investigation showed “a significant number of players participated” in the bounties — by ponying up cash or collecting it — but noted that “the players disciplined participated at a different and more significant level.” Add the losses of Vilma and Smith to the previously announced suspension of head coach Sean Payton for all of 2012, along with shorter penalties for general manager Mickey Loomis and assistant coach Joe Vitt, and NFL Commissioner Roger Goodell came down hard on the Saints ahead of a season that will end with New Orleans hosting the Super Bowl.

As attention to concussions has increased in recent seasons, Goodell has emphasized the importance of player safety via rules enforcement and threats of fines or suspensions. The NFL is facing dozens of lawsuits brought by more than 1,000 former players who say the league didn’t do enough to warn them about — or shield them from — the dangers of head injuries.

If Goodell aims to move on from the bounty case, the NFL Players Association might not let him: The suspended players have three days to appeal, and NFLPA head DeMaurice Smith said the union would fight the ruling. Fujita is a member of the NFLPA’s executive committee who has spoken out in the past about the need for the league to do a better job of protecting players.

Through his agent, Vilma issued a statement saying he is “shocked and extremely disappointed” by the punishment and denying he was a bounty ringleader.

“I never set out to intentionally hurt any player and never enticed any teammate to intentionally hurt another player. I also never put any money into a bounty pool or helped to create a bounty pool intended to pay out money for injuring other players,” Vilma said. He added: “I intend to fight this injustice, to defend my reputation, to stand up for my team and my profession, and to send a clear signal to the Commissioner that the process has failed, to the detriment of me, my teammates, the New Orleans Saints and the game.”

Will Smith also denied a role in the bounties.

“I have never in my career, nor as a captain asked others, to intentionally target and hurt specific opposing players. I was in no way involved in establishing ... a bounty program. The accusations made against me are completely and one-hundred percent false, and I plan to appeal,” he said via statement sent by his publicist. “Through this entire process, the NFL never notified me of what I was being accused of, nor presented me with any evidence or reasoning for this decision. I am interested in discovering who is making these specific and false accusations, and as well as why a decision was made without speaking with me and giving me the opportunity to review the facts.”

DeMaurice Smith said the union “has still not received any detailed or specific evidence from the league of these specific players’ involvement in an alleged pay-to-injure program. We have made it clear that punishment without evidence is not fair. We have spoken with our players and their representatives and we will vigorously protect and pursue all options on their behalf.”

The league said no player agreed to be interviewed in person and the NFLPA did not share information from its own investigation.

According to the NFL, its investigation determined the Saints ran a bounty system for three seasons, with thousands of dollars offered for big hits that sidelined opponents. Originally, the league said 22 to 27 defensive players were involved in the illegal scheme, which was orchestrated by then-Saints defensive coordinator Gregg Williams and started in the season New Orleans won its only Super Bowl championship.

“In assessing player discipline, I focused on players who were in leadership positions at the Saints; contributed a particularly large sum of money toward the program; specifically contributed to a bounty on an opposing player; demonstrated a clear intent to participate in a program that potentially injured opposing players; sought rewards for doing so; and/or obstructed the 2010 investigation,” Goodell said in a statement.

According to the league, Vilma, a linebacker, offered $10,000 in cash to any player who knocked then-Cardinals QB Warner out of a playoff game at the end of the 2009 season, and the same amount for knocking then-Vikings QB Favre out of that season’s NFC championship game. The Saints were flagged for roughing Favre twice in that game, and the league later said they should have received another penalty for a brutal high-low hit from two players that hurt Favre’s ankle. He was able to finish the game, but the Saints won in overtime en route to the NFL title.

Fujita, the NFL said, “pledged a significant amount of money to the prohibited pay-for-performance/bounty pool” during that season’s playoffs. Smith, according to the NFL, “pledged significant sums to the program pool.”

The league said Hargrove “actively obstructed the league’s 2010 investigation into the program by being untruthful to investigators.” He also “actively participated in the program while a member of the Saints,” the league said, adding that he eventually “submitted a signed declaration to the league that established not only the existence of the program at the Saints, but also that he knew about and participated in it.”

Vilma will miss out on $1.6 million in base salary in 2012, while Fujita stands lose more than $640,000, Hargrove more than $385,000, and Smith more than $190,000. Some of their contracts were restructured this offseason, perhaps in anticipation of the punishments.

The Saints, Browns and Packers already have made personnel moves that could help fill the gaps. The Saints signed three linebackers in free agency; the Packers, who also will be without defensive end Mike Neal for four games because he violated the league’s policy on performance-enhancing substances, drafted two defensive linemen last week; and the Browns drafted two linebackers.

“We will respect the Commissioner’s decision. Scott is a valued member of the Cleveland Browns, and we look forward to his participation in our offseason program and training camp,” Browns coach Pat Shurmur said.

The other two clubs did not immediately comment.

Any payout for specific performances in a game, including interceptions or causing fumbles, is against NFL rules. The NFL warns teams against such practices before each season, although in the aftermath of the revelations about the Saints, current and former players from various teams talked about that sort of thing happening frequently — just not on the same scale as was found in New Orleans.

Goodell’s decision was heavily criticized via Twitter by many players. But not all.

“I think he’s doing the right thing to make sure this doesn’t happen ever again. There’s no room for any kind of bounty system in the NFL. It’s a physical sport, and you’ve got to respect the game,” New York Giants quarterback and Super Bowl MVP Eli Manning said. “He’s been harsh, to try to make a statement saying there is no place for this in the game of football.”

James Harrison of the Pittsburgh Steelers, a linebacker suspended by the NFL for a game last season after an illegal hit on Browns quarterback Colt McCoy, tweeted that the penalties were “ridiculous” and suggested that Goodell’s crackdown is motivated by the concussion lawsuits and a desire to increase the regular season to 18 games.

Saints tight end Jimmy Graham tweeted: “I want to see the evidence and hear an explanation.”

Reggie Bush, a running back who played for the Saints from 2006-10 and now is with the Miami Dolphins, wrote on Twitter that the suspensions were “outrageous” and “Next thing you know we’ll be playing two hand touch football! (hash)Lame”

In a memo sent Wednesday to the NFL’s 32 teams, Goodell reminded them that “any program of non-contract bonuses, however it is characterized, is a violation of league rules” and said that every head coach must review those rules with assistants and players during mini-camp or preseason training camp.

Also, all players will be told how they can confidentially report rules violations.

In March, Goodell made Payton the first head coach suspended by the league for any reason, for trying to cover up the system of extra cash payouts. Goodell also indefinitely banned Williams, who was hired in January to run the St. Louis Rams’ defense. Loomis was barred for eight games; Vitt for six. The Saints were fined $500,000 and lost two second-round draft picks.

Fujita, Hargrove and Smith are allowed to participate in offseason activity, including preseason games, before their suspensions take effect. Vilma, though, is suspended immediately and will be reinstated after the coming season’s Super Bowl is played in his team’s city.

“Nothing can be gained from sharing how I feel about” his teammates’ penalties, Saints right tackle Zach Strief said. “I will miss Jonathan very much. Knowing him personally, he’s a good person. This is going to be a tough thing for him to go through. In terms of his leadership, somebody else will step up and take over.”